
where \(\Omega \)  is the union of \(\Omega ^{(r)}\) , see (REF ). Following [1]}, we combine the single-patch preconditioner of (REF ) with an additive Schwarz method. We define a family of local spaces
\(V_h^{(r)}:= \mathrm {span}\left\lbrace  \mathcal {B}_{\text{mp}}^{(r)} \right\rbrace , & & r= 1, \ldots , N_{\mathrm {patch}},\) 
